相关论文: Optimized Schwarz Methods for Maxwell equations
Efficient algorithms for the solution of partial differential equations on parallel computers are often based on domain decomposition methods. Schwarz preconditioners combined with standard Krylov space solvers are widely used in this…
When solving partial differential equations using classical schemes such as finite difference or finite volume methods, sufficiently fine meshes and carefully designed schemes are required to achieve high-order accuracy of numerical…
The discretization of surface intrinsic elliptic partial differential equations (PDEs) poses interesting challenges not seen in flat space. The discretization of these PDEs typically proceeds by either parametrizing the surface,…
We present a two-level overlapping Schwarz preconditioner for three-dimensional problems discretized with the Virtual Element Method. Our approach handles general polyhedral meshes and irregular subdomains, extending the applicability of…
The time harmonic Maxwell equations are of current interest in computational science and applied mathematics with many applications in modern physics. In this work, we present parallel finite element solver for the time harmonic Maxwell…
The dynamic iteration method with a restricted additive Schwarz splitting is investigated to co-simulate linear differential algebraic equations system coming from RLC electrical circuit with linear components. We show the pure linear…
The research of two-level overlapping Schwarz (TL-OS) method based on constrained energy minimizing coarse space is still in its infancy, and there exist some defects, e.g. mainly for second order elliptic problem and too heavy…
Solving time-harmonic wave propagation problems by iterative methods is a difficult task, and over the last two decades, an important research effort has gone into developing preconditioners for the simplest representative of such wave…
This paper derives optimal coefficients for optimized Schwarz iterations for the time-dependent Stokes-Darcy problem using an innovative strategy to solve a nonstandard min-max problem. The coefficients take into account both physical and…
In this article, we prove a sharp estimate for the solutions to parabolic equations on manifolds. Precisely, using symmetrization techniques and isoperimetric inequalities on Riemannian manifold, we obtain a Bandle's comparison on complete…
A preconditioning theory is presented which establishes sufficient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive definite preconditioners. It allows for the analysis and use of non-variational…
We study the peeling of Dirac and Maxwell fields on a Schwarzschild background following the approach developed by the authors in Mason-Nicolas 2009 for the wave equation. The method combines a conformal compactification with vector field…
The discretization of surface intrinsic PDEs has challenges that one might not face in the flat space. The closest point method (CPM) is an embedding method that represents surfaces using a function that maps points in the flat space to…
We employ the method of comparison equations to study the propagation of a massless minimally coupled scalar field on the Schwarzschild background. In particular, we show that this method allows us to obtain explicit approximate expressions…
In this paper, a least-squares finite element method for scalar nonlinear hyperbolic balance laws is proposed and studied. The approach is based on a formulation that utilizes an appropriate Helmholtz decomposition of the flux vector and is…
The Dirichlet-Neumann method is a common domain decomposition method for nonoverlapping domain decomposition and the method has been studied extensively for linear elliptic equations. However, for nonlinear elliptic equations, there are…
We shall derive and propose several efficient overlapping domain decomposition methods for solving some typical linear inverse problems, including the identiffication of the flux, the source strength and the initial temperature in second…
We prove the convergence of greedy and randomized versions of Schwarz iterative methods for solving linear elliptic variational problems based on infinite space splittings of a Hilbert space. For the greedy case, we show a squared error…
We prove linear convergence for a new family of modified Dirichlet--Neumann methods applied to quasilinear parabolic equations, as well as the convergence of the Robin--Robin method. Such nonoverlapping domain decomposition methods are…
Two-phase composites with non-overlapping inclusions randomly embedded in matrix are investigated. A straight forward approach is applied to estimate the effective properties of random 2D composites. First, deterministic boundary value…